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epi.herdtest <- function(se, sp, P, N, n, k){
# Probability of testing positive:
APpos <- P * se + (1 - P) * (1 - sp)
APneg <- (1 - sp)
# Binomial distribution recommended if n / N < 0.2
# Binomial distribution:
bHSe <- 1 - pbinom(q = k - 1, size = n, prob = P)
bHSp <- pbinom(q = k - 1, size = n, prob = 1 - sp)
dbinom <- data.frame(APpos = APpos, APneg = APneg, HSe = bHSe, HSp = bHSp)
# Hypergeometric distribution:
hHSe <- 1 - phyper(k - 1, N * APpos, N - N * APpos, n)
hHSp <- phyper(k - 1, N * APneg, N - N * APneg, n)
dhyper <- data.frame(APpos = APpos, APneg = APneg, HSe = hHSe, HSp = hHSp)
# Sampling fraction:
sfraction <- n / N
rval <- list(sfraction = sfraction, dbinom = dbinom, dhyper = dhyper)
rval
}
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